Inherent gravitational instability of thickened continentalcrust with regionally developed low- to medium-pressure

granulite facies metamorphism

Taras V. Gerya a;b, Walter V. Maresch b;*, Arne P. Willner b,Dirk D. Van Reenen c, C. Andre Smit c

a Institute of Experimental Mineralogy, Russian Academy of Sciences, Chernogolovka, Moscow District 142432, Russiab Institut fu«r Geologie, Mineralogie und Geophysik, Ruhr-Universita«t Bochum, 44780 Bochum, Germany

c Department of Geology, Rand Afrikaans University, Auckland Park, South Africa

Received 27 September 2000; received in revised form 1 June 2001; accepted 6 June 2001

Abstract

Petrological arguments show that regionally developed low- to medium-pressure, high-temperature granulite faciesmetamorphism may critically enhance the lowering of crustal density with depth. This leads to gravitational instabilityof homogeneously thickened continental crust, mainly due to changes in mineral assemblages and the thermalexpansion of minerals in conjunction with the exponential lowering of the effective viscosity of rocks with increasingtemperature. It is argued that crustal processes of gravitational redistribution (crustal diapirism) contributing to theexhumation of granulite facies rocks may be activated in this way. ß 2001 Elsevier Science B.V. All rights reserved.

Keywords: granulites; density; gravity sliding; crust; diapirism

1. Introduction

Numerous structural, geochronological and pet-rological studies have recognized tectono-meta-morphic processes leading to the formation ofgranulite complexes within continental crust (seereviews [1^3]). In a review by Harley [1] of about90 granulite complexes, a remarkable diversity ingranulite characteristics, particularly retrograde

P^T paths, was emphasized. This diversity mirrorsthe variety of tectonic histories of granulites. Henceno single universal tectonic model for the originand exhumation of granulites can be advocated[1].

However, while tectonic models of formation ofdi¡erent granulite complexes are diverse, it iswidely believed that the driving forces operatingduring their geodynamic histories were of externalnature with respect to the continental crust itself.The most important geodynamic processes con-sidered for the origin of granulites are (see reviews[1^3]): (i) tectonic thickening or thinning of thecontinental crust, (ii) magmatic underplating(magmatic accretion), (iii) delamination of cold

0012-821X / 01 / $ ^ see front matter ß 2001 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 1 ) 0 0 3 9 4 - 6

* Corresponding author. Tel. : +49-234-3228155;Fax: +49-234-3214433.

E-mail address: walter.maresch@ruhr-uni-bochum.de(W.V. Maresch).

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mantle lithosphere and (iv) tectonic exhumationof crustal blocks associated with erosion.

In this respect an important addition was madeby Perchuk [4], who emphasized the critical roleof internal crustal buoyancy forces [5] as a factorfor the exhumation of some Precambrian granu-lite terrains. Because of the exponential decreasein the viscosity of rocks with increasing temper-ature (e.g. [6,7]), high-grade granulite facies meta-morphism could trigger processes of crustal dia-pirism [4,5] in gravitationally unstable continentalcrust. The general validity of a gravitational in-stability model for the exhumation of granuliteshas been underlined by numerical geodynamic ex-periments [8], including the numerical modeling ofdi¡erent types of P^T paths [9].

The following major factors for the formationof gravitationally unstable continental crust arediscussed in the literature:

1. magmatic processes:b the invasion of basic magmas in the form

of huge quantities of lava pouring out onthe top of continental crust (e.g. plateaubasalt) or injected as sills, dykes and plu-tons within continental crust [5] ;

b the presence of ma¢c and ultrama¢c vol-canic and plutonic rocks within greenstonebelts situated in the upper portion of cra-tonic successions in granite-greenstonebelts (e.g. [4,5,8]) ;

b the medium-scale (100^4000 m), rhythmicinterlayering of rocks of di¡erent den-sities within the crust, leading to thegrowth of regional diapirs, due to dy-namic interaction of low-density rocksduring gravitational redistribution pro-cesses [8] ;

2. crustal anatexis and granitization processes:b granitoid intrusion, charnockitization and

melting related to high-grade metamor-phism (e.g. [4,5,10]) ;

3. tectonic processes:b selective thickening of the continental

crust in orogenic belts [5] ;b regional stacking of continental crust dur-

ing collision, creating a potentially unsta-ble thickened crust in areas with initially

stable crustal pro¢les (e.g. double-stackedcrust, [11,12]).

This list should be augmented by a considera-tion of the metamorphic phase transformationsthat could also control the formation of region-al-scale gravitational instabilities during high-tem-perature, medium-pressure granulite facies meta-morphism [13]. Phase transformations are oftenconsidered to be a key factor in the increase ofthe density of crustal rocks with increasing meta-morphic grade and depth (e.g. [12,14]). However,the calculations of Bousquet et al. [14] show thatmedium-pressure, two-pyroxene granulites have acharacteristically lower density (by 30^90 kg/m3)than rocks of the same chemical composition atamphibolite facies grade. Therefore, increasingtemperature during prograde granulite metamor-phism may actually produce an inversion of rockdensities with depth. This could be expected tolead to a regional gravitational instability withinan initially stable, homogeneously thickenedcrust. The relationship between the thermal re-gime of metamorphism and gravitational instabil-ity of the continental crust was not discussed byBousquet et al. [14] and needs further investiga-tion.

The major purpose of the present paper is toquantify the in£uence of changes in mineral as-semblages and P^V^T properties of metamorphicminerals on crustal density pro¢les. For this pur-pose, the Gibbs free energy minimization ap-proach (e.g. [15^17]) is used.

2. Methodology

2.1. Compositional and thermal model

In our study we adopted a commonly used one-dimensional generalized model of homogeneouslythickened continental crust [11,12], in which theupper portion is composed of rocks with averagegranodioritic composition [11,12]. Low- to me-dium-pressure granulite facies conditions in ourmodel are assumed to be generated in this gran-odioritic portion of thickened crust at 20^30 kmdepth. The relatively felsic composition of the

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crust undergoing the granulite facies metamor-phism is in accordance with existing data formany granulite regions (see review [1]). In con-trast to the granulite xenolith population heavilydominated by ma¢c compositions, the extensiveoutcrops of granulite terrains are usually domi-nated by felsic to intermediate orthogneisses andmetasediments [1]. As boundary conditions we ac-cepted T = 25³C at the Earth's surface and an as-sumed variable temperature at the boundary be-tween the upper and lower crust at 23^30 kmdepth. Using these conditions, a set of steady-state temperature pro¢les (i.e. geotherms) was cal-

culated for the upper crust (Fig. 1a) according to:

k�D2T=Dz2� �HT � 0 �1�

where z is depth, m, T is temperature, K, k isthermal conductivity of the medium, W/(mWK),and HT is radiogenic heat production in the me-dium, W/m3. The values of k = 2.25 W/(m K) andHT = 2W1036 W/m3 for the upper crust were takenfrom [11].

2.2. Calculation of rock density

In contrast to Bousquet et al. [14], who calcu-lated rock densities for idealized mineral assem-blages, we used the Gibbs free energy minimiza-tion procedure to calculate equilibriumassemblages and compositions of minerals for agiven pressure, temperature and rock composi-tion. The density was then calculated as the ratioof the sum of the molar masses to the sum of themolar volumes of the constituent minerals, whereeach mass and volume is weighted by the molabundance of the mineral in the rock. In pro-gramming the Gibbs free energy minimizationprocedure we adopted an algorithm suggestedby de Capitani and Brown [16] for complex sys-tems containing non-ideal solid solutions. Ther-modynamic data for minerals and aqueous £uidwere taken from the internally consistent databaseof Holland and Powell [21]. Mixing models ofsolid solutions consistent with this database weretaken from the literature [21^24]. Two types ofcalculations were performed: (i) calculation ofpetrogenetic grids and corresponding densitymaps with a resolution of 5 K and 100 bar forT and P, respectively, and (ii) calculation of den-sity pro¢les along geotherms with a resolution of100 m (V30 bar). For crustal density pro¢les,equilibrium assemblages were calculated at tem-peratures v300³C. At lower temperatures the as-semblages calculated for T = 300³C were assumedto be present.

We considered six di¡erent types of metamor-phic rocks as possible major lithologies for thecrust as a whole (Table 1): granodioritic (UC),andesitic (AC) and gabbroic (LC) crust [25],high-grade metapelite (MP) [26], typical Precam-

Fig. 1. Petrogenetic grid (a) and density (kg/m3) map (b) cal-culated for crust of granodioritic composition (see UC in Ta-ble 1). Quartz, plagioclase and Fe^Ti oxides are present inall mineral assemblages. Heavy dashed line in (a) corre-sponds to H2O-saturated granite solidus [18]. Geotherms in(a) (thin lines labelled A^G) are calculated using Eq. 1 atdi¡erent lower boundary conditions: A ^ 500³C at 30 km, B^ 600³C at 30 km, C ^ 700³C at 30 km, D ^ 800³C at 30km, E ^ 900³C at 30 km, F ^ 1000³C at 30 km, G ^ 1000³Cat 23 km. Black solid rectangles in (a) show peak metamor-phic conditions estimated for granulite [19] and amphibolite[20] zones in the Namaqualand granulite terrain (cf. Fig. 8).

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brian granulite (KG) represented by the averagecomposition of the Kanskiy granulite complex,Yenisey Range, Eastern Siberia [27], and the aver-age composition of Archean felsic granulites (FG)[28]. Molar abundances of minerals were calcu-lated from bulk rock compositions (Table 1) usinga system of mass-balance equations for 10 com-ponents: SiO2, TiO2, Al2O3, MgO, Fe2O3, FeO,CaO, Na2O, K2O and H2O. To avoid unrealisticmineral assemblages, cordierite, andalusite andsillimanite had to be considered as unstable inclinopyroxene-normative rocks (UC, AC, LC,FG). For the same reason, calcic amphibole andclinopyroxene were considered unstable in Al-richmetapelites (MP). The system was considered tobe open for H2O [14], i.e. the volatiles producedin dehydration reactions are assumed to be re-moved. Therefore, although £uid phase saturationwas ensured for all calculated equilibrium mineralassemblages such £uids were not involved indensity calculations. P^T-dependent volumes ofphases, V, in equilibrium mineral assemblageswere calculated via the Gibbs potential, G, usingthe thermodynamic relation V = DG/DP and a nu-merical di¡erentiation procedure.

The in£uence of partial melting on gravitation-al instability of the crust has been studied theo-retically using numerical geodynamic modeling(e.g. [10]). In our study we have concentrated onmelt-absent conditions typical for many granulitefacies terrains. In order to simulate these condi-tions, a lowered water activity was assumed at

temperatures above 630³C (cf. granite solidus inFig. 1a) according to the following empiricalequation:

aH2O � 1:03��TK � 203t1�=�t23t1�1:2�0:865 �2�

where t1 = 877+160/(Pkbar+0.348)0:75 and t2 =1262+9Pkbar, 0.16 aH2O 6 1.0. Eq. 2 was cali-brated using data on the P^T parameters of thegranite solidus calculated for di¡erent aH2O [18].This equation allows the granite melting temper-ature to be constrained at 20 K above the giventemperature TK for a given pressure Pkbar andprovides a transition to the conditions of granu-lite facies metamorphism characterized by low-ered water activity [1^3].

3. Results of density calculations

Simpli¢ed petrogenetic grids and correspondingdensity maps obtained for the rocks studied (Ta-ble 1) are presented in Figs. 1^3 and examples ofcalculated crustal density pro¢les are shown inFig. 4. Examples of calculated mineral assemblag-es for speci¢c P^T conditions are presented inTable 2 (see Background Dataset1). Abbreviationsof mineral names are after Kretz [29].

Table 1Rock compositionsa used for density calculations

UCb LCb ACb KGb MPb FGb

SiO2 66.12 54.48 57.94 65.81 65.30 71.34TiO2 0.50 1.00 0.80 0.81 0.81 0.40Al2O3 15.24 16.14 17.94 15.24 17.84 14.57Fe2Oc

3 1.03 2.42 1.70 1.73 1.61 0.71FeO 3.39 7.97 5.62 5.71 5.33 2.35MgO 2.21 6.32 3.50 2.73 2.38 1.11CaO 4.21 8.52 7.49 2.73 1.27 2.83Na2O 3.91 2.81 3.50 2.12 2.02 3.85K2O 3.38 0.34 1.50 3.13 3.44 2.83aIn wt%, sums of oxides normalized to 100%.bAbbreviations used: UC, LC and AC ^ upper granodioritic, lower gabbroic and andesitic crust, respectively [25]; MP ^ typicalhigh-grade metapelite composition [26]; KG ^ average composition of granulites of the Kanskiy complex (Yenisey Range, East-ern Siberia) [27]; FG ^ average composition of Precambrian felsic granulites [28].cFe3� is taken as 25 atomic % from Fe total.

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3.1. In£uence of changes in mineral assemblages

Figs. 1^3 show that the density generally de-creases toward lower pressures and higher temper-atures for all types of rocks. The maximum den-sities are characteristic for greenschist and in partlow-grade amphibolite facies rocks and the mini-mum densities are obtained for high-grade am-phibolite and granulite facies rocks of low tomoderate pressure. The decrease in density withincrease in metamorphic grade is mainly relatedto reactions producing anorthite-rich plagioclase(instead of epidote), sillimanite (instead of kya-nite) and cordierite. This causes a signi¢cant(40^150 kg/m3) decrease in crustal density withdepth for high-temperature geotherms character-ized by low dP/dT gradients (Fig. 4). This de-crease represents the combined in£uence of both

the P^V^T properties of individual minerals aswell as metamorphic reactions. The isolated ef-fects of metamorphic phase transformations, rep-resented by changes in the standard (at T = 25³Cand P = 1 bar) density of di¡erent mineral assem-blages, vary from 20 to 80 kg/m3.

3.2. In£uence of the P^V^T properties of minerals

The in£uence of the P^V^T properties of indi-vidual minerals on crustal density pro¢les wasisolated by calculating densities of minerals andof rocks with ¢xed mineral compositions alongthe geotherms shown in Fig. 1a using the P^V^T equations of Berman [30], Gerya et al. [31] andHolland and Powell [21]. The results indicate thatalong geotherms with relatively low dP/dT gra-dients (e.g. geotherms C^G in Fig. 1a) the densityof rock-forming minerals decreases with depth.The most signi¢cant decrease (40^90 kg/m3) ischaracteristic for Fe^Mg silicates and quartz,while for feldspars this e¡ect is less prominent(10^40 kg/m3). Density pro¢les calculated forgranodioritic crust of constant mineral composi-tion (such as assemblage Kfs+Opx+Cpx in Fig. 1)indicate that the changes in density induced bythe P^V^T properties of individual minerals(20^50 kg/m3) are smaller than, but of the samedirection and order of magnitude as those causedby changes in mineral assemblages (20^80 kg/m3).

3.3. In£uence of continuous metamorphic reactions

Most changes in the mineral assemblages ofmetamorphic rocks proceed via transitionalhigh-variance assemblages. In the case of dehy-dration reactions, the stability ¢elds of these as-semblages may be relatively narrow (9 10 K), de-¢ning abrupt changes in density with increasingtemperature (cf. the transition between Kfs+A-m+Opx and Kfs+Opx+Cpx assemblages in Fig.1a). On the other hand, transitional assemblagescan be stable over a wide range of pressure (1^2kbar) and temperature (50^100 K), providing rel-atively smooth changes in density (cf. the densitydistribution within the Crd+Sil+Kfs+Grt assem-blage in Fig. 2). In both cases, the variation indensity of a rock is related to systematic changes

Fig. 2. Petrogenetic grid (a) and density (kg/m3) map (b) cal-culated for typical high-grade metapelite (see MP in Table1). Quartz, plagioclase and Fe^Ti oxides are present in allmineral assemblages. Heavy dashed lines in (b) mark particu-larly abrupt changes in density related to di¡erences in min-eral assemblage.

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Fig. 3. Density (kg/m3) maps calculated for crust of andesitic (a) and gabbroic (b) composition (see AC and LC in Table 1), aswell as the average compositions of the Kanskiy granulite complex (c) and Precambrian felsic granulites (d) (see KG and FG inTable 1). Heavy dashed lines indicate important changes in mineral assemblages.

Fig. 4. Typical examples of density pro¢les calculated along the geotherms shown in Fig. 1a.

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in the modal amounts of the constituent mineralswith changing P and T.

4. Geodynamic implications

4.1. Degree of potential gravitational instability ofthe crust

On the basis of the results presented above, itcan be concluded that in cases of vertical meta-morphic zoning related to low- to medium-pres-sure granulite facies metamorphism, a consider-able (50^150 kg/m3) decrease in density of rocksshould be a rather common feature in the lowerlevels of upper crust of relatively homogeneouscomposition. This should be especially character-istic for crust of felsic to intermediate composi-tion. In order to quantify this phenomenon interms of gravitational energy, we used a set ofdensity pro¢les calculated for crust of di¡erentcomposition along di¡erent geotherms (Fig. 4).Fig. 4 shows that a zone of lowered density couldappear in thickened upper crust when the temper-ature at its base exceeds 600^700³C. For temper-atures exceeding 800³C, which is typical for me-dium- to low-pressure granulite facies conditions(e.g. [1]), the thickness of the low-density layercould reach 5^15 km, providing a high degree ofinternal gravitational instability for the thickenedcrust.

This degree can be quanti¢ed in terms of themaximum internal gravitational energy that canbe released by gravitational redistribution. Forany given density pro¢le, this value can be esti-mated by comparison to a gravitationally stable`ordered' pro¢le, in which the volume ratios ofrocks with various densities are equivalent butthe density of crust does not decrease with depth.The following equation can then be used to cal-culate the maximum internal gravitational energyof the crust:

U � g=hZ h

z�a�b �z�3b o�z���h3z�dz �3�

where U is mean gravitational energy, J/m3 ;h = 30 000 m is thickness of the upper crust; b(z)

and bo(z) are calculated and theoretical `ordered'density pro¢les with depth z, respectively; g = 9.81m/s2 is acceleration within the gravity ¢eld; a isthe depth for T = 400³C (Vlower limit of green-schist facies [26]). To avoid overestimation of grav-itational energy caused by the possible presence ofnon- or only partially metamorphosed rocks inthe upper portion of the crust at temperatures6 400³C, `ordering' of calculated density pro¢leswas only considered in the a^h depth interval.

Fig. 5a shows the gravitational energy of 30 kmof thickened upper crust as a function of temper-ature at its base. For most of the model crustalcompositions the degree of gravitational instabil-ity increases strongly within the temperature in-terval 600^800³C, which corresponds to high-grade amphibolite and granulite facies conditions.For crust of pelitic composition this increase isshifted to higher temperatures of 800^1000³C,this is related to the stability of low-density, cor-dierite-bearing assemblages (Fig. 2).

The gravitational energy can be compared withthe average calculated enthalpy (Fig. 5b) for rocksalong di¡erent geotherms. The enthalpy of a rockwas calculated as the sum of the molar enthalpiesof the constituent minerals, weighted by the molarabundance of minerals in the rock. The increasein the average enthalpy (Fig. 5b) re£ects the in-crease in the thermal energy of the crust. FromFig. 5 it follows that the calculated increase ingravitational energy of the crust is Vthree ordersof magnitude less than the increase in its thermalenergy. Thus, the production of gravitational in-stability within the crust during high-temperaturemetamorphism requires a negligible part of thethermal energy and does not a¡ect the generalbalance of heat within the crust.

4.2. The e¡ect of viscosity

The possibility of gravitational redistribution inan unstable crust is greatly dependent on its e¡ec-tive viscosity. The viscosity of crustal rocks de-creases exponentially with increasing temperature(e.g. [6,7]) and therefore varies signi¢cantly withdepth, depending on the geothermal gradient. InFig. 6 the viscosity of quartz-bearing rocks com-mon in granulite facies terrains has been calcu-

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Tab

le2

Sele

cted

calc

ulat

ions

ofeq

uilib

rium

min

eral

asse

mbl

ages

and

dens

itie

sof

rock

sfr

omT

able

1

UC

(gra

nodi

orit

ic) U

C1

UC

2U

C3

UC

4

T(³

C)/

P(k

bar)

400/

2.46

500/

3.61

700/

4.89

850/

6.38

Fac

ies

Gre

ensc

hist

Am

phib

olit

elo

w-g

rade

Am

phib

olit

ehi

gh-g

rade

Gra

nulit

e

Rel

ativ

em

olar

abun

danc

eof

min

eral

s(m

ol)

Qtz

=24

.21

Kfs

=2.

89R

t=0.

41Q

tz=

23.3

2K

fs=

4.21

Rt=

0.41

Mag

=0.

42Q

tz=

23.2

5K

fs=

4.21

Rt=

0.41

Mag

=0.

42Q

tz=

19.4

9K

fs=

4.70

Ms=

0.81

KF

e 0:3

2M

g 0:0

8A

l 2:2

0Si

3:40

O10

(OH

) 2P

l=10

.54

Ca 0:3

0N

a 0:7

0A

l 1:3

0Si

2:70

O8

Pl=

10.5

6C

a 0:3

0N

a 0:7

0A

l 1:3

0Si

2:70

O8

Rt=

0.18

Mag

=0.

42Il

m=

0.23

Pl=

9.02

Ca 0:1

5N

a 0:8

5A

l 1:1

5Si

2:85

O8

Bt=

0.48

KF

e 1:1

4M

g 1:8

2A

l 1:0

8Si

2:96

O10

(OH

) 2B

t=0.

48F

e 1:1

6M

g 1:8

0A

l 1:0

8Si

2:96

O10

(OH

) 2P

l=11

.48

Ca 0:2

8N

a 0:7

2A

l 1:2

8Si

2:72

O8

Bt=

1.00

KF

e 1:1

7M

g 1:8

1A

l 1:0

4Si

2:98

O10

(OH

) 2A

m=

0.88

Na 0:9

7C

a 2F

e 1:7

6M

g 3:0

9A

l 1:2

7Si

6:88

O22

(OH

) 2

Am

=0.

87

Na 0:9

5C

a 2F

e 1:7

6M

g 3:1

0A

l 1:2

3Si

6:91

O22

(OH

) 2

Opx

=1.

92F

e 0:7

5M

g 1:2

3A

l 0:0

4Si

1:98

O6

Ep

=1.

21C

a 2F

e 0:6

9A

l 2:3

1Si

3O

12(O

H)

Cpx

=1.

67C

aFe 0:2

5M

gO0:

73A

l 0:0

4Si

1:98

O6

Am

=0.

57

Na 0:9

9C

a 2F

e 1:9

2M

g 2:9

8A

l 1:1

9Si

6:91

O22

(OH

) 2b o

(kg/

m3)a

2758

2721

2721

2734

b 1(k

g/m

3)a

2742

2698

2682

2693

AC

(And

esit

ic)

AC

1A

C2

AC

3A

C4

T(³

C)/

P(k

bar)

400/

2.46

500/

3.61

700/

4.89

850/

6.38

Fac

ies

Gre

ensc

hist

Am

phib

olit

elo

w-g

rade

Am

phib

olit

ehi

gh-g

rade

Gra

nulit

e

Rel

ativ

em

olar

abun

danc

eof

min

eral

s(m

ol)

Qtz

=16

.98

Rt=

0.66

Qtz

=18

.34

Rt=

0.66

Mag

=0.

33Q

tz=

17.2

5K

fs=

0.84

Qtz

=10

.57

Kfs

=2.

11

Ms=

2.11

KF

e 0:2

8M

g 0:0

7A

l 2:3

0Si

3:35

O10

(OH

) 2E

p=

0.91

Ca 2

Fe 0:8

2A

l 2:1

8Si

3O

12(O

H)

Rt=

0.66

Mag

=0.

70R

t=0.

28M

ag=

0.70

Ilm

=0.

38

Pl=

7.84

Ca 0:2

0N

a 0:8

0A

l 1:2

0Si

2:80

O8

Bt=

2.11

KF

e 1:2

0M

g 1:7

5A

l 1:1

0Si

2:95

O10

(OH

) 2P

l=12

.89

Ca 0:5

1N

a 0:4

9A

l 1:5

1Si

2:49

O8

Pl=

14.1

0C

a 0:4

7N

a 0:5

3A

l 1:4

7Si

2:53

O8

Ep

=2.

48C

a 2F

e 0:5

7A

l 2:4

3Si

3O

12(O

H)

Pl=

12.3

3C

a 0:4

5N

a 0:5

5A

l 1:4

5Si

2:55

O8

Bt=

1.27

KF

e 1:1

7M

g 1:7

8A

l 1:1

0Si

2:95

O10

(OH

) 2C

px=

2.15

CaF

e 0:2

5M

g 0:7

2A

l 0:0

6Si

1:97

O6

Chl

=0.

72F

e 1:8

9M

g 3:1

0A

l 2:0

2Si

2:99

O10

(OH

) 8A

m=

0.71

Na 0:9

7C

a 2F

e 1:9

2M

g 2:8

6A

l 1:4

0Si

6:81

O22

(OH

) 2

Am

=1.

15

Na 0:9

3C

a 2F

e 1:7

7M

g 3:0

2A

l 1:3

5Si

6:86

O22

(OH

) 2

Opx

=3.

43F

e 0:7

6M

g 1:2

1A

l 0:0

6Si

1:97

O6

Am

=1.

16

Na 0:9

9C

a 2F

e 1:9

6M

g 2:8

9A

l 1:2

9Si

6:86

O22

(OH

) 2b o

(kg/

m3)a

2892

2826

2809

2835

b 1(k

g/m

3)a

2874

2801

2771

2795

LC

(gab

broi

c)

LC

1L

C2

LC

3L

C4

T(³

C)/

P(k

bar)

400/

2.46

500/

3.61

700/

4.89

850/

6.38

Fac

ies

Gre

ensc

hist

Am

phib

olit

elo

w-g

rade

Am

phib

olit

ehi

gh-g

rade

Gra

nulit

e

Rel

ativ

em

olar

abun

danc

eof

min

eral

s(m

ol)

Qtz

=17

.43

Rt=

0.82

Qtz

=18

.58

Rt=

0.82

Mag

=0.

98Q

tz=

15.2

2R

t=0.

21Il

m=

0.61

Mag

=0.

98Q

tz=

8.05

Kfs

=0.

47

Ms=

0.47

KF

e 0:2

8M

g 0:0

8A

l 2:2

8Si

3:36

O10

(OH

) 2P

l=9.

14C

a 0:5

9N

a 0:4

1A

l 1:5

9Si

2:41

O8

Pl=

10.5

6C

a 0:6

0N

a 0:4

0A

l 1:6

0Si

2:40

O8

Mag

=0.

98R

t=0.

82

Pl=

5.60

Ca 0:1

8N

a 0:8

2A

l 1:1

8Si

2:82

O8

Chl

=0.

71F

e 1:4

4M

g 3:5

2A

l 2:0

8Si

2:96

O10

(OH

) 8B

t=0.

47K

Fe 0:8

2M

g 2:0

6A

l 1:2

4Si

2:88

O10

(OH

) 2P

l=12

.69

Ca 0:5

4N

a 0:4

6A

l 1:5

4Si

2:46

O8

Ep

=3.

12C

a 2F

e 0:6

3A

l 2:3

7Si

3O

12(O

H)

Bt=

0.47

KF

e 1:0

0M

g 1:8

9A

l 1:2

2Si

2:89

O10

(OH

) 2O

px=

2.48

Fe 0:7

6M

g 1:1

9A

l 0:1

0Si

1:95

O6

Opx

=6.

16F

e 0:6

9M

g 1:2

8A

l 0:0

6Si

1:97

O6

Chl

=1.

91F

e 1:7

7M

g 3:2

2A

l 2:0

2Si

2:99

O10

(OH

) 8A

m=

2.23

Na 0:9

6C

a 2F

e 1:5

3M

g 3:0

6A

l 1:7

8Si

6:63

O22

(OH

) 2

Am

=1.

78

Na 0:9

0C

a 2F

e 1:1

4M

g 3:5

1A

l 1:6

0Si

6:75

O22

(OH

) 2

Cpx

=3.

05C

aFe 0:2

2M

gO0:

75A

l 0:0

6Si

1:97

O6

Am

=1.

31

Na 0:9

9C

a 2F

e 1:8

2M

g 3:0

5A

l 1:2

5Si

6:88

O22

(OH

) 2b o

(kg/

m3)a

2943

2898

2927

2952

b 1(k

g/m

3)a

2925

2873

2886

2908

EPSL 5900 20-7-01

T.V. Gerya et al. / Earth and Planetary Science Letters 190 (2001) 221^235228

Tab

le2

(con

tinu

ed)

MP

(met

apel

itic

)

MP

1M

P2

MP

3M

P4

T(³

C)/

P(k

bar)

400/

2.46

500/

3.61

700/

4.89

850/

6.38

Fac

ies

Gre

ensc

hist

Am

phib

olit

elo

w-g

rade

Am

phib

olit

ehi

gh-g

rade

Gra

nulit

e

Rel

ativ

em

olar

abun

danc

eof

min

eral

s(m

ol)

Qtz

=37

.37

Rt=

0.68

Mag

=0.

66Q

tz=

38.1

9R

t=0.

68M

ag=

0.68

Qtz

=38

.77

Kfs

=2.

06Si

l=4.

39Q

tz=

28.7

1K

fs=

4.90

Sil=

0.91

Pl=

5.76

Ca 0:2

4N

a 0:7

6A

l 1:2

4Si

2:76

O8

Pl=

5.88

Ca 0:2

6N

a 0:7

4A

l 1:2

6Si

2:74

O8

Rt=

0.68

Mag

=0.

68R

t=0.

68M

ag=

0.68

Chl

=1.

35F

e 2:1

1M

g 2:8

4A

l 2:1

0Si

2:95

O10

(OH

) 8C

hl=

1.21

Fe 2:0

6M

g 2:7

6A

l 2:3

6Si

2:82

O10

(OH

) 8P

l=5.

88C

a 0:2

6N

a 0:7

4A

l 1:2

6Si

2:74

O8

Pl=

5.80

Ca 0:2

5N

a 0:7

5A

l 1:2

5Si

2:75

O8

Ms=

4.90

KF

e 0:1

2M

g 0:0

3A

l 2:7

0Si

3:15

O10

(OH

) 2M

s=4.

52K

Fe 0:0

9M

g 0:0

3A

l 2:7

6Si

3:12

O10

(OH

) 2B

t=2.

84K

Fe 1:1

9M

g 1:3

9A

l 1:8

4Si

2:58

O10

(OH

) 2G

rt=

1.33

Ca 0:0

6F

e 1:8

7M

g 1:0

7A

l 2Si

3O

12

Ep

=0.

06C

a 2F

e 0:6

8A

l 2:3

2Si

3O

12(O

H)

Bt=

0.38

KF

e 1:2

6M

g 1:3

2A

l 1:8

4Si

2:58

O10

(OH

) 2C

rd=

1.70

Fe 0:5

2M

g 1:4

8A

l 4Si

5O

18(H

2O

) 0:3

9

b o(k

g/m

3)a

2772

2771

2794

2752

b 1(k

g/m

3)a

2755

2744

2747

2717

FG

(ave

rage

fels

icgr

anul

ite)

FG

1F

G2

FG

3F

G4

T(³

C)/

P(k

bar)

400/

2.46

500/

3.61

700/

4.89

850/

6.38

Fac

ies

Gre

ensc

hist

Am

phib

olit

elo

w-g

rade

Am

phib

olit

ehi

gh-g

rade

Gra

nulit

e

Rel

ativ

em

olar

abun

danc

eof

min

eral

s(m

ol)

Qtz

=34

.84

Kfs

=1.

51R

t=0.

33Q

tz=

34.7

6K

fs=

2.84

Qtz

=34

.76

Kfs

=2.

91Q

tz=

31.8

1K

fs=

3.91

Pl=

9.24

Ca 0:1

4N

a 0:8

6A

l 1:1

4Si

2:86

O8

Rt=

0.33

Mag

=0.

29R

t=0.

10Il

m=

0.23

Mag

=0.

29Il

m=

0.33

Mag

=0.

29

Ms=

1.73

KF

e 0:3

3M

g 0:0

8A

l 2:1

8Si

3:41

O10

(OH

) 2P

l=11

.33

Ca 0:2

9N

a 0:7

1A

l 1:2

9Si

2:71

O8

Pl=

11.3

3C

a 0:2

9N

a 0:7

1A

l 1:2

9Si

2:71

O8

Pl=

11.3

5C

a 0:2

9N

a 0:7

1A

l 1:2

9Si

2:71

O8

Ep

=0.

82C

a 2F

e 0:7

1A

l 2:2

9Si

3O

12(O

H)

Bt=

1.08

KF

e 1:3

2M

g 1:6

4A

l 1:0

8Si

2:96

O10

(OH

) 2B

t=1.

00K

Fe 1:2

0M

g 1:7

6A

l 1:0

8Si

2:96

O10

(OH

) 2O

px=

1.47

Fe 0:7

6M

g 1:2

2A

l 0:0

4Si

1:98

O6

Bt=

0.68

KF

e 1:2

1M

g 1:7

7A

l 1:0

4Si

2:98

O10

(OH

) 2A

m=

0.01

Na 0:9

8C

a 2F

e 2:2

2M

g 2:6

1A

l 1:3

2Si

6:85

O22

(OH

) 2

Am

=0.

01

Na 0:9

5C

a 2F

e 1:8

3M

g 3:0

2A

l 1:2

5Si

6:90

O22

(OH

) 2

Cpx

=0.

01C

aFe 0:2

5M

gO0:

73A

l 0:0

4Si

1:98

O6

Am

=0.

17

Na 0:9

9C

a 2F

e 2:0

7M

g 2:8

2A

l 1:2

1Si

6:90

O22

(OH

) 2b o

(kg/

m3)a

2721

2676

2676

2685

b 1(k

g/m

3)a

2704

2652

2633

2641

KG

(ave

rage

Kan

skiy

gran

ulit

e)

KG

1K

G2

KG

3K

G4

T(³

C)/

P(k

bar)

400/

2.46

500/

3.61

700/

4.89

850/

6.38

Fac

ies

Gre

ensc

hist

Am

phib

olit

elo

w-g

rade

Am

phib

olit

ehi

gh-g

rade

Gra

nulit

e

Rel

ativ

em

olar

abun

danc

eof

min

eral

s(m

ol)

Qtz

=36

.00

Rt=

0.67

Mag

=0.

20Q

tz=

39.9

5R

t=0.

67M

ag=

0.72

Qtz

=39

.55

Sil=

0.93

Kfs

=1.

28Q

tz=

30.0

6K

fs=

4.39

Pl=

5.18

Ca 0:1

3N

a 0:8

7A

l 1:1

3Si

2:87

O8

Pl=

7.73

Ca 0:4

2N

a 0:5

8A

l 1:4

2Si

2:58

O8

Rt=

0.67

Mag

=0.

72R

t=0.

67M

ag=

0.72

Bt=

0.68

KF

e 1:2

3M

g 1:7

5A

l 1:0

4Si

2:98

O10

(OH

) 2B

t=2.

93K

Fe 1:1

7M

g 1:5

1A

l 1:6

4Si

2:68

O10

(OH

) 2P

l=7.

73C

a 0:4

2N

a 0:5

8A

l 1:4

2Si

2:58

O8

Pl=

7.61

Ca 0:4

1N

a 0:5

9A

l 1:4

1Si

2:59

O8

Ep

=1.

27C

a 2F

e 0:8

1A

l 2:1

9Si

3O

12(O

H)

Ms=

1.46

KF

e 0:1

0M

g 0:0

3A

l 2:7

4Si

3:13

O10

(OH

) 2B

t=3.

11K

Fe 1:1

5M

g 1:4

4A

l 1:8

2Si

2:59

O10

(OH

) 2O

px=

2.03

Fe 0:7

2M

g 1:1

2A

l 0:3

2Si

1:84

O6

Chl

=1.

03F

e 2:0

5M

g 2:9

4A

l 2:0

2Si

2:99

O10

(OH

) 8C

rd=

0.40

Fe 0:4

1M

g 1:5

9A

l 4Si

5O

18(H

2O

) 0:3

9M

s=3.

71K

Fe 0:3

1M

g 0:0

7A

l 2:2

4Si

3:38

O10

(OH

) 2G

rt=

1.20

Ca 0:0

9F

e 1:6

1M

g 1:3

0A

l 2Si

3O

12

b o(k

g/m

3)a

2806

2775

2768

2797

b 1(k

g/m

3)a

2789

2748

2721

2755

ab o

isst

anda

rdde

nsit

yat

298

Kan

d1

bar

(i.e

.w

itho

utP

^V^T

cont

ribu

tion

ofin

divi

dual

phas

es),b 1

isde

nsit

yat

Tan

dP

give

n.

EPSL 5900 20-7-01

T.V. Gerya et al. / Earth and Planetary Science Letters 190 (2001) 221^235 229

lated along di¡erent geotherms, using experimen-tally calibrated rheological equations written inthe form [7] :

O � ADc n exp �3E=RT� �4�

R � 106c=�2O � �5�

where R is viscosity, Pa s, O is strain rate, s31, c isstress, MPa, E is activation energy, kJ/mol, AD ismaterial constant, MPa3n/s, n is a power-law con-stant and R is the gas constant. Parameters forEq. 4 for some minerals and rocks were takenfrom the summary by Ranalli [7]. In our calcula-tion we used a moderate value for the strain rateof 10314 s31 (e.g. [7,34]). From the data of Fig. 6it follows that low dP/dT geotherms are charac-terized by a strong (two to four orders of magni-tude) decrease in viscosity at the bottom of thick-ened upper crust for all rock types considered,forming a rheologically weak zone (e.g. [7,34]).Further decreases in viscosity of high-grade rockscould also be related to partial melting (e.g. [10])

or to the local (e.g. within shear zones) presenceof water-bearing £uids (compare results for dryand wet granite and quartzite in Fig. 6a,b). Inthe case of a gravitational redistribution processthe strain rate could vary signi¢cantly in time andspace (e.g. [10]), thus a¡ecting the e¡ective viscos-ity of rocks. Although the viscosity pro¢les shownin Fig. 6 are therefore not suitable for the directestimation of e¡ective viscosity of rocks duringcrustal diapirism, it can be argued that a high(10^1000) viscosity contrast between upper (cooland strong) and lower (hot and weak) portions ofthe crust should be a rather common feature ofgranulite facies metamorphism. In such a case thedevelopment of a crustal-scale gravitational redis-tribution process would be de¢ned by the e¡ectiveviscosity of relatively strong low-grade rocks inthe upper portion of the crust [5].

4.3. Time-scale estimates

To estimate semi-quantitatively the possiblerates of gravitational redistribution as a function

Fig. 5. Gravitational energy (a) and average enthalpy (b) of 30 km of thickened upper crust of various bulk compositions (Table1) as a function of temperature at its base. Lettering of geotherms as in Fig. 1a.

EPSL 5900 20-7-01

T.V. Gerya et al. / Earth and Planetary Science Letters 190 (2001) 221^235230

of the e¡ective viscosity of the upper (low-grade)portion of the crust, a simple model proposed byRamberg [5] can be used (Fig. 7a). It is assumedthat along a low dP/dT geotherm (e.g. geothermsC^F in Fig. 1a) an inverted step-like distributionof density with depth is characteristic (see Fig.4a). This distribution can be approximated by atwo-layer model with an initial geometry and withboundary conditions as shown in Fig. 7a. A lowernon-slip boundary condition is assumed at thebottom of the homogeneous crust. An uppernon-slip boundary condition is assumed at an ar-bitrary level suggested by the signi¢cant increasein viscosity with decreasing depth (Fig. 6a,b). It isalso assumed that the initial sinusoidal distur-bance of the boundary between the two layersof di¡erent density within the crust is of smallamplitude (A) and characteristic wavelength (V)[5]. This provides conditions for investigating thegrowth of the diapir as de¢ned [5] by the equa-tion:

y � A exp �tW�b 23b 1�WK WH Wg=�2R 2�� �6�

where y is the height of the diapir, m; t is time, s;

H is the thickness of each layer, m; R2 is theviscosity of the diapir, Pa s; K is the factor ofgrowth [5] depending on viscosity contrast. Tak-ing into account the calculated density pro¢les(e.g. Fig. 4a), H = 10 000 m and (b23b1) = 100kg/m3 were accepted and A was taken to be500 m. According to the calculated variations ofviscosity with depth (Fig. 6), a high viscositycontrast of R1/R2 = 10^500 was used for estima-tion of K = 0.032 (R1/R2 = 10) and K = 0.00065(R1/R2 = 500) [5]. Fig. 7b shows the height of thediapir as a function of time for di¡erent valuesof R1 and R1/R2. According to these results, aprocess of gravitational redistribution driven byinstabilities induced by phase transformationsand thermal expansion of minerals would proceedin realistic time scales on the order of 10^50 Myrat a viscosity of the upper low-grade portion ofthe crust on the order of 1020^1021 Pa s.

Therefore, the initiation of the crustal-scaleprocess of gravitational redistribution requires alowering of the viscosity of low-grade rocks to1020^1021 Pa s, which could be achieved by thesimultaneous in£uence of an increase in temper-ature, tectonic stress and £uid/melt activity during

Fig. 6. Viscosity of some quartz-bearing rocks calculated along the geotherms of Fig. 1a at a strain rate of 10314 s31 from theexperimentally determined rheological parameters given in [7]. The thick gray line limiting the viscosity pro¢les denotes the brit-tle^ductile transition calculated as `Mohr^Coulomb viscosity' [32] at a strain rate of 10314 s31 after Byerlee's law [33].

EPSL 5900 20-7-01

T.V. Gerya et al. / Earth and Planetary Science Letters 190 (2001) 221^235 231

the prograde stage of high-grade metamorphism.On the other hand, in the case of weak zonescutting through the upper crust, the rate of grav-itational redistribution could be much higher. Forexample, for the process of fast (within about9 Myr) buoyant uplift of medium-pressure gran-ulites along a weak tectonic zone, moderate valuesof the e¡ective viscosity of upper crustal low-grade rocks (1021 Pa s) and granulites (1019 Pas) were estimated using the shapes of retrogradeP^T paths of metapelites from the Limpopo high-grade terrain [9].

5. Discussion and possible geological examples

As follows from Figs. 1^4 the decrease in den-sity of major rock types with depth should be arather common feature in crust with low- to me-dium-pressure, high-temperature metamorphism.However, the actual formation of gravitationallyunstable density pro¢les within continental crustwill also depend on the evolution of the geother-

mal gradient, on changes in chemical compositionof the crust with depth and on the kinetics ofmetamorphic phase transformations (especiallyin the upper low-grade portion of the crust, inwhich a high-density layer can form). Further-more, possible gravitational redistribution will de-pend on the evolution of the degree of gravita-tional instability and the e¡ective rheology ofthe crust during and after high-grade metamor-phism. It can be argued that the gravitational in-stability of the crust related to metamorphic phasetransformations may in many respects be similarto the instability induced by partial melting of thecrust (e.g. [10]). For high-grade metamorphiccomplexes, both sources of instability should beconsidered as an important factor that may cru-cially a¡ect the dynamics of exhumation of high-grade rocks.

A mechanism of buoyant exhumation of gran-ulites driven by the lithological di¡erence betweenupper and lower crustal rocks has already beensuggested for several medium-pressure Precambri-an granulite complexes, i.e. the Limpopo granulitecomplex in South Africa [35], the Lapland com-plex in the Kola Peninsula [35], the Sharizhalgaycomplex in the Baikal area, Eastern Siberia [4],the Kanskiy granulite complex in the YeniseyRange, Eastern Siberia [36]. Considering the rela-tively felsic bulk composition of these complexes(e.g. KG in Table 1), metamorphic phase trans-formations should be considered to be an addi-tional factor, thus increasing the degree of grav-itational instability of the crust during high-temperature, medium-pressure metamorphism.

An excellent example of an extensive low-pres-sure granulite terrain characterized by an ex-tremely low dP/dT gradient (compare geothermG in Fig. 1a) may be found in the NamaquaMobile Belt of the NW Cape province of SouthAfrica. This granulite terrain of the BushmanlandSubprovince is exposed as a long-wavelength,E^W-trending, dome-like structure of 150^180km width (Fig. 8), gradually passing into upperamphibolite facies rocks that overly the granulitesto the N and S [19,37]. The boundary betweenboth facies areas is the cordierite+garnet+K-feld-spar+sillimanite-in-isograd. The granulite and theoverlying amphibolite terrains are of similar over-

Fig. 7. Modeled diapir growth for a two-layered case [5]. (a)Initial design of the model and boundary conditions. (b) Theheight of a diapir as a function of time calculated using Eq.6 at R1/R2 = 10 (thin lines) and R1/R2 = 500 (thick lines).

EPSL 5900 20-7-01

T.V. Gerya et al. / Earth and Planetary Science Letters 190 (2001) 221^235232

all rock composition, dominated chie£y byquartz^feldspar gneisses, minor metapelites andquartzites, as well as subordinate metabasitesand iron formations, thus indicating an overallgranodioritic composition. The granulite terrainis also characterized by a considerable amountof partial melt generated by dehydration melting.In the center of the granulite area, about 1000km2 of hercynite^quartz facies rocks occur, indi-cating an exceptionally wide outcrop of high-tem-perature rocks [37]. Peak metamorphic conditionswere around 850³C and 5 kbar [19], passing grad-ually over a distance of 200 km to overlying am-phibolite facies rocks with 680³C and 4 kbar [20]as peak conditions. The area is characterized by

42 km of crust, with 25 km of predominantlyma¢c lower crust [38]. Waters [19,37] and Willner[20] interpret the origin of this belt as stacking ofan Andean-type convergent margin, with the highgeotherm being produced by magmatic underplat-ing. Penetrative deformation in the entire area isprior to the peak of metamorphism, and relatedto stacking with a general top to SW (Fig. 8)tectonic movement, with abundant pre- and syn-kinematic intrusions of calcalkaline granitoids[39,40]. Although there is no evidence for a de-crease of P at high T preserved in the granulitesthemselves [37], such a conclusion can be drawnfrom the amphibolite terrain [20]. The subhori-zontal foliation produced by stacking was subse-quently refolded to large-scale megafolds of kmwavelength (including small-scale steep struc-tures). This is the only retrograde deformationat high temperature and involves relatively smallamounts of horizontal shortening, accommodatedby some vertical extension [41]. There is no indi-cation of retrograde extensional deformation orlater orogenesis contributing to the extremelyslow (E100 Myr) exhumation of the granulites[37]. At and after the peak of metamorphism, theNamaqua granulites were at a depth level of 12^15 km, where the density of the dominant felsicquartz-bearing rocks under this extreme geother-mal gradient must have been considerably lessthan that of the upper crust according to Figs.1b and 4a. Considering the markedly long periodof cooling, generally slow buoyant uprise of high-grade rocks by about 4 km relative to the amphib-olite facies terrain (Fig. 7b) to produce the ex-posed metamorphic zonation seems realistic(Fig. 8).

6. Conclusion

It can be concluded that metamorphic phasetransformations proceeding with increasing tem-perature should be considered as a possible sourceof gravitational instability of the continental crustwhen low dP/dT geotherms are characteristic.Thus, low- to medium-pressure granulite faciesmetamorphism might be `genetically' related toan increase in the degree of gravitational instabil-

Fig. 8. Structural^metamorphic characteristics of the Nama-qualand granulite complex. Abbreviations: BS ^ Bushman-land Subprovince, RS ^ Richersvelt Subprovince, GS ^ Gor-donia Subprovince, K ^ Kheis Belt, KP ^ Kaapvaal Craton.

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ity within initially stable homogeneously thick-ened continental crust. Metamorphic phase trans-formations, partial melting and thermal expansionof minerals can be expected to accompany expo-nential lowering of the e¡ective viscosity of rockswith increasing temperature. This can lead to theactivation of crustal processes of gravitational re-distribution (crustal diapirism) that in turn resultin signi¢cant displacement and complex deforma-tion of metamorphic rocks within the crust (e.g.[4,5,8^10,13,42^44]). This suggests a strong linkbetween external collisional and internal gravita-tional mechanisms of rock deformation in high-grade metamorphic regions. Since collisionalmechanisms should be operative during the earlyprograde stages of a tectono-metamorphic cycle,causing thickening of the crust and a correspond-ing increase in radiogenic heat supply, gravita-tional mechanisms can be expected to dominateduring the later thermal peak and retrogradestages, providing an important factor for the ex-humation of granulite facies rocks.

Acknowledgements

This work was carried out as part of an RF-RSA scienti¢c collaboration supported by RFBRGrant # 00-05-64939 to T.V.G., by FRD andGencor grants to D.D.V.R., and by an Alexandervon Humboldt Foundation Research Fellowshipto T.V.G. We also acknowledge support by theGerman Research Society through SFB 526. Theauthors are grateful to J. Connolly, J. Dixon andanonymous reviewers for their valuable sugges-tions, resulting in substantial improvements tothe manuscript, and to B.J. Wood for able edito-rial support.[BW]

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